269edo

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269edo

270edo →

Prime factorization	269 (prime)
Step size	4.46097¢
Fifth	157\269 (700.372¢)
Semitones (A1:m2)	23:22 (102.6¢ : 98.14¢)
Dual sharp fifth	158\269 (704.833¢)
Dual flat fifth	157\269 (700.372¢)
Dual major 2nd	46\269 (205.204¢)
Consistency limit	3
Distinct consistency limit	3

269 equal divisions of the octave (abbreviated 269edo or 269ed2), also called 269-tone equal temperament (269tet) or 269 equal temperament (269et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 269 equal parts of about 4.46 ¢ each. Each step represents a frequency ratio of 2^1/269, or the 269th root of 2.

269edo is inconsistent in the 5-odd-limit and the errors of both harmonics 3 and 5 are quite large. The patent val tempers out 6144/6125 in the 7-limit, 540/539 and 5632/5625 in the 11-limit and 364/363 and 676/675 in the 13-limit. The 269c val tempers out 225/224 and 4375/4374 in the 7-limit, and 269ce 385/384 in the 11-limit, so that it supports and provides an excellent tuning for catakleismic and marvel temperaments.

Odd harmonics

Approximation of odd harmonics in 269edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	-1.58	+1.79	-0.80	+1.29	+1.84	-1.87	+0.21	+2.11	+1.37	+2.08	+0.72
	relative (%)	-35	+40	-18	+29	+41	-42	+5	+47	+31	+47	+16
Steps (reduced)		426 (157)	625 (87)	755 (217)	853 (46)	931 (124)	995 (188)	1051 (244)	1100 (24)	1143 (67)	1182 (106)	1217 (141)

Subsets and supersets

269edo is the 57th prime edo.